Question

Jason takes off from rest across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.10. Unfortunately, the skis run out of fuel after only 11 s. How far has Jason traveled when he finally coasts to a stop

Answer 1

The total distance traveled by body is = 274.41 m

Step-by-step explanation:

Given :

Combined mass
`m = 75` Kg

Thrust force
`F_(t) =` 200 N

Coefficient of kinetic friction
`\mu _(k) =` 0.10

According to newton's law

`F_(t) - \mu m g = ma`

`200 - 0.1 * 75 * 9.8 = 75 a` ( ∵
`g = 9.8 (m)/(s^(2) )` )

Before run out of fuel the acceleration is,

`a = (126.43)/(75) = 1.69(m)/(s^(2) )`

Distance covered in 11 sec. is given by,

`y = v_(0)t + (1)/(2)at^(2)`

Where
`y =` distance,
`v_(0) =` initial velocity =
`0`,
`a =` acceleration,

`y = (1)/(2) * 1.69 * (11) ^(2)`

`y = 102.24` m

After run out of fuel velocity of body is,

`v = v_(o) + at`

Where
`v_(o) =` 0

`v = 1.69 * 11 = 18.37 (m)/(s)`

After fuel run out of only frictional force act on body,

`ma = \mu_(k) m g`

Acceleration is given by,

`a = 0.1 * 9.8`

`a = 0.98 (m)/(s^(2) )`

So distance traveled by body after run out of fuel is given by

`v^(2) - v_(o) ^(2) =2ax`

Where initial velocity
`v_(o) =` 0,

`x = (337.46)/(1.96)`

`x = 172.17` m

So total distance traveled by body is,

`d = 172.17 +102.24 = 274.41` m